Relativity and simple algebra II

Just brushing up on my Epstein (a space-propertime diagram) on a forum from 2017. I guess I didn't understand the high level of discussion going on in the background and that what I superficially think Epstein is showing about c is up for deeper debate. Interesting how bangstrom is arguing c is a dimensional constant and not a velocity that is constant from all perspectives. Epstein diagrams seem to support non-constancy of c as a velocity.

Ok here is the Minkowski diagram of Alice's round trip converted to an Epstein diagram:

I underestimated the power of this depiction and how much Minkowski fudged his diagram so that it would be forced into agreement with Einstein's assumptions to explain the MMX result. All the Epstein diagram does is swap the ct and ct' axes such that the main equation is re-written as $$(ct)^2 = (ct')^2 + x^2$$ sum of squares rather than difference of squares. Notice how similar it looks to the reverse-Minkowski and I'm sure when I do the reverse-Epstein (Earth/Bob as the stationary ct'=axis) it will look very similar to the standard Minkowski diagram. Notice how the green Loedel proper simultaneity lines are still half speed (but inverse sign) at -1/3c . Notice how the pink and yellow light lines are the same length during constant relative velocity before t'=4. Notice their slope is not 45 degrees and that the v=c line is 0 degrees, not 45. Epstein doesn't accommodate the assumption that c is the same slope from all perspectives. It also doesn't care about the velocity combo law. When Alice turns to go back to earth, her velocity relative to earth is simply twice ( v=6/5c, Yv=6/4c) earth's initial relative velocity to Alice (v=3/5c, Yv=3/4c). Yet conversion back to Minkowski gives the values expected by relativity. The meaning behind all this is significant but it'll take some time for me to figure it out its deeper meaning.

ralfcis:

Good, I've never heard of celerity before but I like the term proper velocity. Your v'=x'/t' but since your x'=Yx and your t'=t/Y, your $$v'= Y^2x/t = Y^2v$$ (probably not if one of my perspectives for x' or t' is wrong).
Your analysis is not correct here, but it would take me another lengthy post to do a full derivation to show clearly what you did wrong. Remember that when we're dealing with the length of anything, including a measured length a "start" line and a "finish" line for some journey, two spacetime events are involved when we're just dealing with one reference frame, corresponding to the locations in space of the two lines and the simultaneous time that those two locations are measured. If we then want to look at the same journey in a different frame, then a third spacetime event usually needs to be introduced, because the events that simultaneously mark the locations of the "start" and "finish" lines in one frame will not be simultaneous in the different frame. Therefore, the two frames will not agree on the "length" of the journey, or on the time taken for a spaceship, say, to make the journey.

In the Alice/Bob example of Alice taking a trip, relativity shows that, during the trip, if Bob says that Alice's spaceship is travelling at constant velocity v at all relevant times, then Alice will say that Bob is travelling at velocity -v at all relevant times.

I've already said v=x/t is a relative velocity and Yv =x/t'=x/(t/Y) is not. Can you not see the difference between the equations?
Don't be silly. It was me who pointed out exactly what the difference is, in the first place. You're responding to my post #98, where I explained exactly what the difference is, and even put a label on the quantity $\gamma v$.

You won't accept any number of papers that Brehme velocity or celerity or proper velocity or Yv is valid in relativity because you've been unaware of it and anything you've been unaware of can't be valid.
Don't try to put words in my mouth, please.

I have no problem with "proper velocity" or "celerity" or whatever you want to call it being valid in relativity, as long as we all understand what we're talking about when we use that concept. That is, as long as you accept the definition in post #98, I have no problem with it at all.

As for me being previously unaware of it, that's not true. I was a little silly in that I didn't think of it previously. That was probably because it came up in this thread in an unusual context. In the general theory of relativity - or in the 4-vector formulation of special relativity - proper velocity is important in defining a number of important physical quantities, which relativistically preserve certain important types of conservation laws and the like.

I have never heard it referred to as "Brehme velocity" before. I've never heard of "Loedel lines", either. The various texts and research papers on relativity that I have read have not used those terms, and they did not come up in my formal studies of relativity.

I won't call Yv as v' anymore to avoid confusion with the definition of v' in relativity, ok?
Okay. The main thing is that we both work to make sure we understand each other. If we think we're talking about the same thing when really we're talking about two different things, that makes the conversation a waste of time for both of us.

I'll stick with Y not $$\gamma$$ because I have to be consistent with my spacetime diagrams.
It's fine. I'll assume that when you write Y, it's the same as $\gamma$. That is:

$Y=\gamma=\frac{1}{\sqrt{1-(v/c)^2}}=\frac{c}{\sqrt{c^2-v^2}}=\frac{c}{\sqrt{(c+v)(c-v)}}= \dots$

Okay. The main thing is that we both work to make sure we understand each other. If we think we're talking about the same thing when really we're talking about two different things, that makes the conversation a waste of time for both of us.
I have no formal training only Brian Greene's online course I linked here. I have partly read 1 book, Relativity for Engineers but it was mostly General Relativity. My biggest obstacle is common terminology.

ralfcis:

No, v is the relative velocity of Bob and Alice relative to each other. But since there are the background frame and the Earth frame as 2 additional participants, there are other relative velocities depicted.
The Earth frame is the same as Bob's frame, isn't it?

Bob is stationary at all times relative to the Earth, in your scenario in which Alice travels out from Earth and back again while Bob stays on Earth.

What is this "background frame" you mention? Who or what is stationary in the "background frame"?

I may draw Alice leaving earth at 3/5c and Bob at 0c but their relative velocity is 3/5 even if, in the Loedel diagram, each of their velocities are labelled as -1/3c and +1/3c their relative velocity is 3/5c.
Can you please show me how you calculate 3/5c from -1/3c and +1/3c?

What is the frame of the "Loedel diagram". Can you show me a "Loedel diagram"? What is a "Loedel diagram"?

The universe is not really, physically whizzing past you. It is always stationary relative to you without invoking a preferred frame or absolute motion as so often comes out of the mouths of those who have zero understanding of relativity. In relativity, Alice and Bob take turns being the stationary frame and yes I understand there is no such thing as stationary in relativity. But since I can choose a depiction that represents all others, I choose the Earth frame as stationary without implication of a preferred frame.
That's all fine. I'm happy to refer to the Earth/Bob frame as "stationary" and the Alice frame as "moving". We both agree that, in Alice's frame, Alice considers herself "stationary" and Bob to be "moving".

We also both seem to agree that there are no preferred frames - no frame is "absolutely" at rest. I don't know what the "background frame" is that you mentioned above, though.

Relativity is stuck on the example of 2 astronauts floating past each other in a deep featureless space with no distance markers and being unable to determine who is actually moving.
No. It's not stuck on that.

You have no choice but to draw relative velocity as absolute velocity so no more niggling comments that there's no such thing as absolute velocity.
All I'm saying is there's nothing in the universe we can point to and say "that's absolutely at rest". You agree with that, don't you?

All spacetime diagrams have at least 4 participants, not just 2 as is shown in relativity's useless 2 astronaut example.
It seems to me that in your Alice and Bob example, we only need Alice and Bob. Why do we need two more "participants"?

Here is a reverse-Minkowski of Alice returning to Earth with Alice as the stationary frame (except she's not stationary and neither is the earth).
But your red "Alice" line in that diagram is in motion in the 'x' coordinates of your diagram, so this diagram doesn't show Alice as "stationary".

Purists will say I've drawn it backwards (look at the signs on the x-axis) and what are these blue and red numbers?
Yes, because most diagrams like this are drawn with the x coordinate increasing to the right, whereas yours increases to the left. Yours is a kind of mirror-image diagram, compared to what we usually see.

They're to show that once Alice is deemed the stationary frame, she is not actually on Earth past time 0. Earth has taken off from her, not she from it.
We agree that, from Alice's perspective, she stays still and Earth flies away from her.

She occupies a blank space where Earth used to be. This blank space is the background cartesian coordinates and it is one of the participants.
All of space is "blank" in this scenario, except for Alice and Bob (or Earth, if you prefer). It's not clear what your "background coordinates" are attached to. Who or what is stationary in your "background" coordinates? Is there anything?

Even though the entire universe is whizzing past Alice, space is not...
Space isn't a substance. You can't measure the speed of "space".

...because, as I showed in my vacuum bottle example, you can't move a vacuum...
A vacuum is a region of space that contains nothing. You can't move "nothing", so I guess it's okay to say you can't move a vacuum.

It's sort of the same thing as saying you can't move the hole in a doughnut. The hole isn't a thing you can move. The doughnut is a thing you can move.

..., there is no relative velocity to space and, by the transitive property, to the light that propagates through it using it as a non-material electromagnetic medium.
I agree about space. Light, on the other hand, can be thought of as little particles: photons. Those are things that can move from one place to another.

What the drawing then shows is after occupying empty space for 4 red years she takes off to return to Earth which is speeding away from her at 3/5c. Her relative velocity to Earth was -3/5c in the regular Minkowski diagram so this means she must chase earth at 15/17c (relative to the blank space)...
Relative to the blank space? The blank space is not a thing. You just said that, didn't you?

The important thing here is a participant is someone who can set his time on his clock as the reference time for everyone else (the other 3 participants).
I don't know what you mean by that. Clocks in different frames tick at different rates, but given coordinates of a spacetime event in any one frame, all other frames can always calculate what the equivalent coordinates of the event would be according to their own clocks.

Look back at the Loedel conversion to Minkowski.
Could you please supply the equations or transformations you use to convert to a "Loedel" diagram or frame, or whatever it is?

Next up, the equivalent Epstein depiction to show the assumptions of relativity are irrelevant to correctly depicting the physics.
Really?

What are the alternative postulates you're using for your "Epstein depiction"?

As far as I can tell, Epstein diagrams are fully consistent with the "assumptions of relativity".

The Minkowski diagram was doctored to support the assumptions of time dilation and length contraction, the Epstein was not.
In what way was it "doctored"?

Are you saying that Minkowski diagrams are incorrect, or tell lies, or something?

ralfcis:

Just brushing up on my Epstein (a space-propertime diagram) on a forum from 2017. I guess I didn't understand the high level of discussion going on in the background and that what I superficially think Epstein is showing about c is up for deeper debate. Interesting how bangstrom is arguing c is a dimensional constant and not a velocity that is constant from all perspectives. Epstein diagrams seem to support non-constancy of c as a velocity.
This is the first time I've come across Epstein diagrams.

I've done a little reading up on them. As far as I can tell, they are just another way of illustrating spacetime events, using a system of polar coordinates rather than Cartesian ones. They are fully consistent with special relativity.

I do not believe that Epstein supports/supported the "non-constancy of c as a velocity". Epstein diagrams seem to assume that c is the same in all frames, consistent with SR.

I think you might be unnecessarily tying yourself in knots trying to understand Epstein diagrams, especially when you seem so confused about the basics of the Alice/Bob example.

I suggest that, in our ongoing conversation, we leave discussion of Epstein until late - at least until after you have responded to my posts #58 and/or #71/72.

When are you going to get to those, by the way? Do I have to wait months? A year?

Above, you claimed you were responding to my post #27, but then you went off onto this tangent about "reverse Minkowski" diagrams and then Epstein, so that you didn't really respond to my post at all.

Do you think you can possibly stay focussed long enough to try responding directly to the points I put to you in posts #71 and 72, say? Could you please try that now?

I underestimated the power of this depiction and how much Minkowski fudged his diagram so that it would be forced into agreement with Einstein's assumptions to explain the MMX result.
Minkowski didn't fudge his diagram. What are you talking about? Minkowski diagrams are straightforward. They just plot space on one coordinate axis (one dimension only, obviously), and time on the other axis (or ct, which is just a "scaled" time coordinate).

All the Epstein diagram does is swap the ct and ct' axes such that the main equation is re-written as $$(ct)^2 = (ct')^2 + x^2$$ sum of squares rather than difference of squares.
As far as I can tell, so far from my reading on this, that's not all it does.

But we can discuss this later.

You should realise that Epstein's book, in which he introduces his diagrams, is an idiosyncratic, non-mainstream view of relativity. It's not "wrong", but it requires careful reading. Here's an extract from one review:

The myth is introduced with the idea of “enabling the inquiring mind to feel at home in a mysterious universe” (page 77). It is a unique and appealing idea, and it works. We are asked to believe that everything always travels at the speed of light. When an object is “at rest”, it is actually traveling at the speed of light through time; as speed through space increases, speed through time decreases. By imagining the arrow that describes the velocity as rotating in a space-time diagram, the results of the first 4 chapters can indeed be easily visualized. The myth has some problems, however.

Dr. Epstein never clearly points out that his space-time diagram is not the standard space-time diagram. Maybe this doesn’t matter to a reader who has no professional interest in the subject, but if any readers go on to study relativity seriously, they will be very confused. The myth seems to blur the distinction between proper time and coordinate time, in particular the fact that proper time is different for each different reference frame seems to get lost when Epstein talks about the twin paradox, especially in figure 5-11. His description of the resolution of the paradox occurs in a figure caption and is very weak. His attempt to explain the reasons behind the myth fails dismally.​

As I feared, most of your latest questions were already answered. This thread will either balloon exponentially or you can ask the questions in a way that shows you've attempted to answer them for yourself from what I've actually already written. I will continue answering you questions once in order if I feel they have not already been answered.

I have no formal training only Brian Greene's online course I linked here. I have partly read 1 book, Relativity for Engineers but it was mostly General Relativity. My biggest obstacle is common terminology.
My advice would be to forget about general relativity completely at first, and just concentrate on special relativity.

The mathematics of special relativity only requires algebra, for the most part. To understand general relativity, on the other hand, you need to be very familiar with calculus, for starters. It also helps to have a good understanding of linear algebra. Many physics majors who encounter general relativity for the first time at Masters or PhD level usually find that they have to learn all about tensor calculus from scratch, as well as lots of technical stuff about metrics, affine connections and other esoteric mathematical topics.

If I were you, I'd get a decent book that just covers special relativity, first.

Here's a really good one you can download for free. At least one of the writers is a giant in the field of relativity:

http://www.eftaylor.com/spacetimephysics/

As I feared, most of your latest questions were already answered.
Well, maybe I'm just not understanding your answers. It doesn't look to me like you've answered most of my questions.

I'd appreciate it if you could respond point-by-point to posts #71 and 72, saying which parts you agree with and which parts you disagree with. That would be very helpful in narrowing down the territory in which we might potentially disagree.

For the most part, it seems like your numerical results reproduce the results of special relativity. That's not surprising, since for the most part you seem to be using the equations of special relativity to calculate things.

What I'm trying to figure out is where you think SR has problems, or is wrong. You talk of things like Minkowski "fudging" his diagrams, for example, but you don't point to anything specific that would show any "fudging". And then, occasionally, you make claims that relativity is "stuck" on something or can't deal with some problem you think you've cracked, but when questioned on specifics you just start talking about something different.

This thread will either balloon exponentially or you can ask the questions in a way that shows you've attempted to answer them for yourself from what I've actually already written.
I've already done that. Where your analysis has generated different answers to the ones SR would provide, I have shown you how SR would calculate its answers, so you can compare.

You are very welcome to point out any errors you have found in SR's methods, or in my use of SR in analysing your scenarios. I invite you to do that.

You complain about the thread ballooning, but you keep introducing new material and new ideas all the time, without ever dealing with objections to one of your ideas or calculations or graphs before moving on to present a different one, or three.

Look: it's easy. I'm making it easy for you. Forget that we're up to post #109. Just respond to posts #71 and 72. Just two posts out of 100. And we'll see how we go after that.

If, on the other hand, you're unwilling or unable to engage with my objections at this time, for whatever reason, then I'll stop wasting my time for now. I'll leave you to think about what I have written, and if you ever come up with some answers to questions and objections I have put to you, we can talk about it after you finally respond.

Ok 71 and 72 next.

#71
Before I get into the details, I want to tell you the main problem that I'm seeing in your analysis. It is that, while you take into account the different rate at which A's clock ticks relative to B's (i.e. time dilation), you do not take into account that A's measurements of distance are also different from B's. The reason you end up concluding that light signals travel faster than c in A's frame is because you're using the wrong distance units in A's frame. Specifically, instead of using A's rulers, you want A to use B's rulers. You can't do that and get consistent results.
You mean like I'm proposing a math alternative to relativity's math, which depends on time dilation and length contraction to maintain the constancy of c from all perspectives, without using relativity's math.

Your link is confused to me so I am guessing (note GUESSING) you yourself do not have a method of measuring the speed of light with a one way measurement

Happy to be proven incorrect

First, I don't know where you get v'=Yv from. That is an incorrect expression for transforming velocities between reference frames.
You also need to be careful to distinguish the velocity of some object or person inside a reference frame from the velocity of the frame itself.
v=0 inside a frame always.
This is what the special relativistic velocity addition formula does - it allows us to transform velocities of objects between two reference frames. I should also note that, according to special relativity (hereafter referred to as SR), the speed of anything that travels at velocity c in one frame must be c in every other frame.
"Loedel lines" are equivalent to SR's lines of simultaneity, although in several posts above you have made errors when drawing those lines.
AA. Stop calling things you don't understand "errors". Loedel lines of simultaneity are not lines of perspective from any of the 4 participants.
I should point out that the "Loedel lines" on your graph look like* SR lines of simultaneity for Alice (A).
AA. They are not that at all. They join proper times.
Bob's (B's) lines of simultaneity are horizontal lines on that graph. SR lines of simultaneity, in general, connect points with the same time coordinate in a given frame.
AK. next you'll ask me what AA and AK mean.
* P.S. Further down, you will see that I discovered that your "Loedel lines" are not the same as SR lines of simultaneity, after all. I'm not sure what they are, now.
AA. Try reading or using the search button to re-read.
whether you agree with my definition of "proper time"
AA. Proper time is within a frame. Co-located frames share proper times even though they may not be the same value. My Loedel perspective allows one to peek into proper times of separated frames. Relativity forbids that but math does not.
Notice that I have used SR length contraction to calculate the "contracted" distance for the trip in A's frame of reference.
Notice I didn't need to. Yv takes care of all that for me.
Your graph, though, doesn't show A's length measurements.
Length contraction is due to relativity of simultaneity so the x'-axis is Alice's line of perspective simultaneity. I'll include that if I need to make a comparison to SR but this is not SR, I use Loedel lines of proper simultaneity although there is no such concept in SR.
themselves as travelling at 0.75c.
Completely false. Alice uses Bob's star charts and her clock to "see" herself moving at 3/4c. What she can't see is the length of her path contract. What she does see is a physical planet outside her window that marks from both hers and Bob's perspectives she is at the 3ly point. There are durations and points. She can't look back and see her path has shrunk but she knows what point she's at. In case you're wondering, I have no need for lorentz transforms because my math does not need rotated coordinates.
A must use coordinate x', in her own frame.
Again and again and again, that's SR, that's not what I use in this thread so stop trying to shoehorn this into relativity. If you believe my problem is I don't understand relativity then you're wasting my time.
The encoded message from A will be "I have reached the finish line at the 1.2 ly mark
Wrong again. She has no on-board odometer. She has star charts the same as Bob's which both agree the mark is 1.5ly away for the purposes of the message. If she says 1.2ly away then according to Bob she hasn't reached the finish line yet. It's a time trial, what if her velocity was wavering, would Bob need to figure out her position from her perspective from her DSR? That's insane.
Instead, the "finish line" travels towards her at a speed of (3/5)c
No, not instead. I can pick any Minkowski diagram of the relative velocity and I did not choose the one you're switching to.
it seems bizarre of you to claim that time was running at the same rate for both A and B.
It seems bizarre that you can't understand that from the Md's I've provided. Are you reading these posts covering your eyes peeking between your fingers? You read my stuff redacting everything that doesn't fit with the philosophy of relativity while I'm talking plain old algebra. It's like I took an engine out of a blue car and put it in a red car and you keep arguing those engines only belong in blue cars.
why would their watches end up showing different times? We're assuming these are well-calibrated atomic clocks, aren't we? What went wrong with them?
AA. relativity of simultaneity affected when the stopwatches were pressed at the end. You're just not getting any of this at all. You told me you know how to read spacetime diagrams yet now I see you can only read spacetime diagrams you've seen before.
SR doesn't have "hyperbolic lines of proper time simultaneity".
AA. Yes I've shown the example of that. The hyperbolic lines intersect all velocity lines at the same proper time. You can't connect this with what you said here?
(ct)2&#x2212;x2" role="presentation" style="display: inline-table; line-height: normal; font-size: 14.6667px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(ct)2−x2(ct)2−x2, which obviously has both space and time components, not just time. That quantity is essentially similar to what, in SR, is called the "spacetime interval". Note carefully: spacetime interval, which is not the same as time interval.
Stop with the condescension. We don't know how much each one knows but I at least treat you like you have the basic popular understanding of relativity. You think if I didn't I'd be able to draw spacetime diagrams when almost no one on any forum I've been on can do that?

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Your analysis is not correct here, but it would take me another lengthy post to do a full derivation to show clearly what you did wrong.
Here's what I did wrong. Length contraction and time dilation are from 2 different perspectives as shown in the following MD.

As opposed to (extrapolated from how relativity uses the terms)

Dilation is from the reference frame's direct perspective but contraction is from the reference frame's perspective through the moving frame's perspective.
So if time dilation is t=Yt' (2.5=5/4*2), length dilation is x=Yx' (2.5=5/4*2) . But length contraction is x=Y(Yx") (2.5=5/4(5/4*1.6)).
For dilation t'=t/Y, x'=x/Y but for contraction x"=x/Y^2.

So for relativity v'= x'/t' = (x/Y)/(t/Y) = x/t. Get it? I don't.

GUESSING) you yourself do not have a method of measuring the speed of light with a one way measurement
I added the part where you take the measurement while still in motion to avoid permanent age difference even though it would be an insignificant but calculable amount.

#72
Why should there be equivalency?
Look at my football example. If you are going for a long bomb, the reduced relative velocity to the football is measured by the initial distance separation over the time the ball is in the air. (No one on the planet seems to understand this.) The same thing is happening in my Md. Everything is the same, the light football takes longer to reach the receding ship but the definition of relative velocity has changed because if it hadn't the ship's relative velocity to the light football would have been reduced just as in a normal football. (This has nothing to do with Einstein's assumption of the constancy of c from all perspectives but is an inescapable result of the Fizeau experiment and the resultant relatvistic velocity combo equation pre-Einstein.) Yet the effects of relative velocity to light are still evident by the imbalance of light durations between the pink and yellow signals when drawn as Md but not when drawn as Ld or Ed. The prime rule here is that any spacetime diagram of relative velocity must yield the same physical results yet there is no physical difference in light durations for the Ld or Ed depictions. This results from the general ignorance of the difference between velocity and relative velocity (and I'll throw "closing speed" in there while I'm at it).

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#72
Your graph wrongly indicates that the pink signal was sent at 2 years on A's clocks. In fact, it was sent at 2.5 years, according to A's clocks. That means the green line on your graph is not a line of simultaneity for A. Your "Loedel lines", whatever they are, aren't lines of simultaneity at all, but something else.
AA. I hope you understand now.
I would appreciate it if you explained what your "Loedel lines" are. Previously I assumed they were lines of simultaneity.
AA
Again, you're ignoring the fact that A's frame doesn't use B's rulers.
In other words, it might all come back to your error in assuming that A and B share the same rulers.
AA. Yeah let's ignore but not ignore the same irrelevant point over and over.
I am still not clear on whether you are trying to replace SR by your own theory, with your own theory having a variable speed of light. Is that what you're trying to do?
Not even close. You seem to assume using different measuring devices makes the thing you're measuring variable.
I don't understand how you justify applying a Y factor to any v. What are you doing when you do that?
AA
No! Alice's clocks run at different rates from Bob's clocks; you agree with this, apparently. Alice's rulers also are not the same lengths as Bob's rulers; you appear to be consistently ignoring this.
No and yes.
one that is not consistent with SR or with real-world experiments.
false
Define "proper year".
AA
You're clearly using the term "proper time" in a completely non-standard way. Please define it.
No and AA
Difficult to understand until you post your definition of "proper time".
AA but why it's difficult is that having a perspective of something that has no perspective seems like an oxymoron. It's a perspective of something that is unmeasurable in the present moment but it is calculable and those calculations correspond to the numbers the Loedel perspective is revealing.

So I did as you asked, I will continue from where I left off on #27 which is the reverse-Epstein diagram (not easy so far).